English
Related papers

Related papers: State-based nested iteration solution of optimal c…

200 papers

In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order…

Optimization and Control · Mathematics 2024-05-09 Yongcheng Dai , Bangti Jin , Ramesh Sau , Zhi Zhou

We present a dynamic model for the optimal control problem (OCP) of hydrogen blending into natural gas pipeline networks subject to inequality constraints. The dynamic model is derived using the first principles partial differential…

Optimization and Control · Mathematics 2024-02-27 Saif R. Kazi , Kaarthik Sundar , Anatoly Zlotnik

Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential…

This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…

Numerical Analysis · Mathematics 2016-11-16 Wei Gong , Ningning Yan , Zhaojie Zhou

We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and state restrictions, in the sense that differential…

Optimization and Control · Mathematics 2019-04-02 Pablo Pedregal

We consider a control constrained parabolic optimal control problem and use variational discretization for its time semi-discretization. The state equation is treated with a Petrov-Galerkin scheme using a piecewise constant Ansatz for the…

Optimization and Control · Mathematics 2015-03-09 Nikolaus von Daniels , Michael Hinze , Morten Vierling

This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning, where the primary design objective is to minimize the…

Optimization and Control · Mathematics 2017-04-24 Richard C. Barnard , Christian Clason

This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and…

Numerical Analysis · Mathematics 2016-12-09 Tracy Babb , Adrianna Gillman , Sijia Hao , Per-Gunnar Martinsson

In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form \begin{eqnarray*} \frac{\partial y}{\partial t} + A y &=& \int_0^t B(t, s) y(s) ds + Gu,…

Optimization and Control · Mathematics 2016-06-14 Anil Kumar , Amiya K. Pani , Mohan C. Joshi

We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…

Optimization and Control · Mathematics 2010-08-24 Morten Vierling

This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…

Numerical Analysis · Mathematics 2020-04-07 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

We consider an optimal control problem governed by a rate-inde\-pendent system with non-convex energy. The state equation is approximated by means of viscous regularization w.r.t.\ to hierarchy of two different Hilbert spaces. The…

Optimization and Control · Mathematics 2026-01-12 Merlin Andreia , Christian Meyer

In this paper, elliptic control problems with integral constraint on the gradient of the state and box constraints on the control are considered. The optimal conditions of the problem are proved. To numerically solve the problem, we use the…

Optimization and Control · Mathematics 2018-10-05 Zixuan Chen , Xiaoliang Song , Bo Yu , Xiaotong Chen

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…

Optimization and Control · Mathematics 2023-04-06 Caroline Geiersbach , Teresa Scarinci

In this work, we present a numerical solver for optimal control problems constrained by linear and semi-linear second-order elliptic PDEs. The approach is based on recasting the problem and includes an extension of Uzawa's algorithm to…

Numerical Analysis · Mathematics 2024-10-24 Charalambos G. Makridakis , Aaron Pim , Tristan Pryer

The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…

Optimization and Control · Mathematics 2023-07-04 Enrique Otarola

In this paper we study optimal control problems with either fractional or regional fractional $p$-Laplace equation, of order $s$ and $p\in [2,\infty)$, as constraints over a bounded open set with Lipschitz continuous boundary. The control,…

Optimization and Control · Mathematics 2017-01-20 Harbir Antil , Mahamadi Warma

This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough $L^\infty$ coefficients, which has important applications in composite materials and geophysics. We use one of the…

Numerical Analysis · Mathematics 2024-12-20 Yanping Chen , Jiaoyan Zeng , Xinliang Liu , Lei Zhang

Optimal Control Problems consist on the optimisation of an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation…

Optimization and Control · Mathematics 2024-01-09 Ashutosh Bijalwan , Jose J Muñoz

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang